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Discrete curvature and torsion from cross-ratios Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2021-01-21 Christian Müller, Amir Vaxman
Motivated by a Möbius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular Möbius invariant point-insertion-rule, comparable to the classical four-point-scheme, we construct circles along discrete curves. Asymptotic analysis shows that these circles defined on a sampled
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H 4 -Solutions for the Olver–Benney equation Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2021-01-19 Giuseppe Maria Coclite, Lorenzo di Ruvo
The Olver–Benney equation is a nonlinear fifth-order equation, which describes the interaction effects between short and long waves. In this paper, we prove the global existence of solutions of the Cauchy problem associated with this equation.
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Automorphisms of $$\mathbb{C}^m$$ C m with bounded wandering domains Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2021-01-11 Luka Boc Thaler
We prove that the Euclidean ball can be realized as a Fatou component of a holomorphic automorphism of \(\mathbb{C}^m\), in particular as the escaping and the oscillating wandering domain. Moreover, the same is true for a large class of bounded domains, namely for all bounded simply connected regular open sets \(\Omega \subset \mathbb{C}^m\) whose closure is polynomially convex. Our result gives in
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Lagrangian submanifolds of the complex hyperbolic quadric Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2021-01-08 Joeri Van der Veken, Anne Wijffels
We consider the complex hyperbolic quadric \({Q^*}^n\) as a complex hypersurface of complex anti-de Sitter space. Shape operators of this submanifold give rise to a family of local almost product structures on \({Q^*}^n\), which are then used to define local angle functions on any Lagrangian submanifold of \({Q^*}^n\). We prove that a Lagrangian immersion into \({Q^*}^n\) can be seen as the Gauss map
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On the arithmetic Cohen–Macaulayness of varieties parameterized by Togliatti systems Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2021-01-06 Liena Colarte-Gómez, Emilia Mezzetti, Rosa M. Miró-Roig
Given any diagonal cyclic subgroup \(\Lambda \subset \text {GL}(n+1,k)\) of order d, let \(I_d\subset k[x_0,\ldots , x_n]\) be the ideal generated by all monomials \(\{m_{1},\ldots , m_{r}\}\) of degree d which are invariants of \(\Lambda\). \(I_d\) is a monomial Togliatti system, provided \(r \le \left( {\begin{array}{c}d+n-1\\ n-1\end{array}}\right)\), and in this case the projective toric variety
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Explicit formula on function fields and application: Li coefficients Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2021-01-04 Kajtaz H. Bllaca, Kamel Mazhouda
In this note, we formulate an explicit formula for the completed zeta function of a function field K of genus g over a finite field \(\mathbb {F}_q\), analogous to the Weil explicit formula. Then we give an arithmetic formula for the nth Li coefficient \(\lambda _{K}(n)\) for the function field K. Furthermore, as an application, we give some formulas for the Euler–Stieltjes constants \(\gamma _{K}\)
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Functional calculus on non-homogeneous operators on nilpotent groups Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-12-29 Mattia Calzi, Fulvio Ricci
We study the functional calculus associated with a hypoelliptic left-invariant differential operator \(\mathcal {L}\) on a connected and simply connected nilpotent Lie group G with the aid of the corresponding Rockland operator \(\mathcal {L}_0\) on the ‘local’ contraction \(G_0\) of G, as well as of the corresponding Rockland operator \(\mathcal {L}_\infty \) on the ‘global’ contraction \(G_\infty
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Geodesic connectedness of affine manifolds Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-10-12 Ivan P. Costa e Silva, José L. Flores
We discuss new sufficient conditions under which an affine manifold \((M,\nabla )\) is geodesically connected. These conditions are shown to be essentially weaker than those discussed in groundbreaking work by Beem and Parker and in recent work by Alexander and Karr, with the added advantage that they yield an elementary proof of the main result.
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Low Mach and thin domain limit for the compressible Euler system Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-10-09 Matteo Caggio, Bernard Ducomet, Šárka Nečasová, Tong Tang
We consider the compressible Euler system describing the motion of an ideal fluid confined to a straight layer \(\Omega _{\delta }=(0,\delta )\times {\mathbb {R}}^2, \ \ \delta >0\). In the framework of dissipative measure-valued solutions, we show the convergence to the strong solution of the 2D incompressible Euler system when the Mach number tends to zero and \(\delta \rightarrow 0\).
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Standing waves with prescribed mass for the coupled Hartree–Fock system with partial confinement Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-10-08 Huifang Jia, Xiao Luo
In this paper, we focus on the standing waves with prescribed mass for the coupled Hartree–Fock system, which is the basic quantum chemistry model of small number of electrons interacting with static nuclei. This leads to study the normalized solutions to the following nonlocal elliptic system $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\Delta u+(x_{1}^{2}+x_{2}^{2}+\cdot \cdot \cdot
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Generalized Cauchy–Kovalevskaya extension and plane wave decompositions in superspace Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-10-08 Alí Guzmán Adán
The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the biaxial Dirac operator \(\partial _{\mathbf{x}} +\partial _{\mathbf{y}}\). In the classical commuting case, this result can be written as a power series of Bessel type of certain differential operators acting on a single initial function. In the superspace setting, novel structures appear in the cases of negative
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Asymptotic behaviour for local and nonlocal evolution equations on metric graphs with some edges of infinite length Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-10-07 Liviu I. Ignat, Julio D. Rossi, Angel San Antolin
We study local (the heat equation) and nonlocal (convolution-type problems with an integrable kernel) evolution problems on a metric connected finite graph in which some of the edges have infinity length. We show that the asymptotic behaviour of the solutions to both local and nonlocal problems is given by the solution of the heat equation, but on a star-shaped graph in which there are only one node
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Invariance of basic Hodge numbers under deformations of Sasakian manifolds Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-10-07 Paweł Raźny
We show that the Hodge numbers of Sasakian manifolds are invariant under arbitrary deformations of the Sasakian structure. We also present an upper semi-continuity theorem for the dimensions of kernels of a smooth family of transversely elliptic operators on manifolds with homologically orientable transversely Riemannian foliations. We use this to prove that the \(\partial {\bar{\partial }}\)-lemma
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Global Denjoy–Carleman hypoellipticity for a class of systems of complex vector fields and perturbations Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-10-03 Bruno de Lessa Victor, Alexandre Arias Junior
We characterize global Denjoy–Carleman hypoellipticity for the family of systems acting on the torus \({\mathbb {T}}_{t}^{N} \times {\mathbb {T}}_{x}\) given by \(L_{j} = \frac{\partial }{\partial t_{j}} + \left( a_{j}(t_{j}) + ib_{j}(t_{j}) \right) \frac{\partial }{\partial x} + \lambda _j\) , where \(a_j, b_j\) are real-valued \(2\pi\)-periodic elements of the classes and \(j = 1, 2,\ldots , N\)
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Magnetic trajectories on tangent sphere bundle with g-natural metrics Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-08-25 Mohamed Tahar Kadaoui Abbassi, Noura Amri, Marian Ioan Munteanu
We study magnetic trajectories in the unit tangent sphere bundle with pseudo-Riemannian g-natural metrics of a Riemannian manifold. A high interest is dedicated to the case when the base manifold is a space form and when the metric is of Kaluza–Klein type. Slant curves are obtained when a certain conservation law is satisfied. We give a complete classification of slant magnetic curves (respectively
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Characters of $$\pi '$$ π ′ -degree and small cyclotomic fields Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-08-24 Eugenio Giannelli, Nguyen Ngoc Hung, A. A. Schaeffer Fry, Carolina Vallejo
We show that every finite group of order divisible by 2 or q, where q is a prime number, admits a \(\{2, q\}'\)-degree nontrivial irreducible character with values in \({\mathbb{Q}}(e^{2 \pi i /q})\). We further characterize when such character can be chosen with only rational values in solvable groups. These results follow from more general considerations on groups admitting a \(\{p, q\}'\)-degree
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On geometric estimates for univalent functions Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-08-17 Eva A. Gallardo-Gutiérrez, Christian Pommerenke
We provide geometric estimates for conformal maps of the unit disc. As a consequence, a bound for the derivative of such maps follows yielding, in particular, an answer to a question posed by Martín Chuaqui. Finally, estimates regarding the curvature of image arcs under conformal maps are also obtained.
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Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-08-11 Wei Dai, Guolin Qin
In this paper, we establish various maximum principles and develop the method of moving planes for equations involving the uniformly elliptic nonlocal Bellman operator. As a consequence, we derive multiple applications of these maximum principles and the moving planes method. For instance, we prove symmetry, monotonicity and uniqueness results and asymptotic properties for solutions to various equations
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Lifespan estimates for local in time solutions to the semilinear heat equation on the Heisenberg group Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-08-09 Vladimir Georgiev, Alessandro Palmieri
In this paper, we consider the semilinear Cauchy problem for the heat equation with power nonlinearity in the Heisenberg group \(\mathbf {H}_n\). The heat operator is given in this case by \(\partial _t-\varDelta _{{{\,\mathrm{H}\,}}}\), where \(\varDelta _{{{\,\mathrm{H}\,}}}\) is the so-called sub-Laplacian on \(\mathbf {H}_n\). We prove that the Fujita exponent \(1+2/Q\) is critical, where \(Q=2n+2\)
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Taylor spectrum approach to Brownian-type operators with quasinormal entry Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-08-09 Sameer Chavan, Zenon Jan Jabłoński, Il Bong Jung, Jan Stochel
In this paper, we introduce operators that are represented by upper triangular \(2\times 2\) block matrices whose entries satisfy some algebraic constraints. We call them Brownian-type operators of class \({\mathcal {Q}},\) briefly operators of class \({\mathcal {Q}}.\) These operators emerged from the study of Brownian isometries performed by Agler and Stankus via detailed analysis of the time shift
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Maximal Cohen–Macaulay tensor products Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-08-07 Olgur Celikbas, Arash Sadeghi
In this paper, we are concerned with the following question: if the tensor product of finitely generated modules M and N over a local complete intersection domain is maximal Cohen–Macaulay, then must M or N be a maximal Cohen–Macaulay? Celebrated results of Auslander, Lichtenbaum, and Huneke and Wiegand yield affirmative answers to the question when the ring considered has codimension zero or one,
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Strong conciseness of coprime and anti-coprime commutators Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-22 Eloisa Detomi, Marta Morigi, Pavel Shumyatsky
A coprime commutator in a profinite group G is an element of the form [x, y], where x and y have coprime order and an anti-coprime commutator is a commutator [x, y] such that the orders of x and y are divisible by the same primes. In the present paper, we establish that a profinite group G is finite-by-pronilpotent if the cardinality of the set of coprime commutators in G is less than \(2^{\aleph _0}\)
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A characterization of weak L p -eigenfunctions of the Laplacian on homogeneous trees Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-21 Pratyoosh Kumar, Sumit Kumar Rano
In this article, we characterize all eigenfunctions of the Laplacian on homogeneous trees, which are the Poisson transform of \(L^p\) functions defined on the boundary. Using the duality argument, we also proved the restriction theorem for the Helgason–Fourier transforms on a homogeneous tree.
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A group theoretic proof of a compactness lemma and existence of nonradial solutions for semilinear elliptic equations Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-20 Leonardo Biliotti, Gaetano Siciliano
Symmetry plays a basic role in variational problems (settled, e.g., in \({\mathbb {R}}^{n}\) or in a more general manifold), for example, to deal with the lack of compactness which naturally appears when the problem is invariant under the action of a noncompact group. In \({\mathbb {R}}^n\), a compactness result for invariant functions with respect to a subgroup G of \(\mathrm {O}(n)\) has been proved
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On the Hewitt–Stromberg measure of product sets Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-18 Omrane Guizani, Amal Mahjoub, Najmeddine Attia
In this paper, we shall be concerned with evaluation of Hewitt–Stromberg measure of Cartesian product sets by means of the measure of their components. This is done by the construction of new multifractal measures, on the Euclidean space \({\mathbb {R}}^n\), in a similar manner to Hewitt–Stromberg measures but using the class of all n-dimensional half-open binary cubes of covering sets in the definition
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The Poisson equation on Riemannian manifolds with weighted Poincaré inequality at infinity Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-15 Giovanni Catino, Dario D. Monticelli, Fabio Punzo
We prove an existence result for the Poisson equation on non-compact Riemannian manifolds satisfying weighted Poincaré inequalities outside compact sets. Our result applies to a large class of manifolds including, for instance, all non-parabolic manifolds with minimal positive Green’s function vanishing at infinity. On the source function, we assume a sharp pointwise decay depending on the weight appearing
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Hermitian curvature flow on complex locally homogeneous surfaces Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-12 Francesco Pediconi, Mattia Pujia
We study the Hermitian curvature flow of locally homogeneous non-Kähler metrics on compact complex surfaces. In particular, we characterize the long-time behavior of the solutions to the flow. We also provide the first example of a compact complex non-Kähler manifold admitting a finite time singularity for the Hermitian curvature flow. Finally, we compute the Gromov–Hausdorff limit of immortal solutions
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Functional analysis and exterior calculus on mixed-dimensional geometries Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-12 Wietse M. Boon, Jan M. Nordbotten, Jon E. Vatne
We are interested in differential forms on mixed-dimensional geometries, in the sense of a domain containing sets of d-dimensional manifolds, structured hierarchically so that each d-dimensional manifold is contained in the boundary of one or more \(d + 1\)-dimensional manifolds. On any given d-dimensional manifold, we then consider differential operators tangent to the manifold as well as discrete
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The Gröbner fan of the Hilbert scheme Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-07-09 Yuta Kambe, Paolo Lella
We give a notion of “combinatorial proximity” among strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. We show that this notion guarantees “geometric proximity” of the corresponding points in the Hilbert scheme. We define a graph whose vertices correspond to strongly stable ideals and whose edges correspond to pairs of adjacent ideals. Every term order induces an orientation
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On the characterization of the space of derivations in evolution algebras Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-30 Yolanda Cabrera Casado, Paula Cadavid, Mary Luz Rodiño Montoya, Pablo M. Rodriguez
We study the space of derivations for some finite-dimensional evolution algebras, depending on the twin partition of an associated directed graph. For evolution algebras with a twin-free associated graph, we prove that the space of derivations is zero. For the remaining families of evolution algebras, we obtain sufficient conditions under which the study of such a space can be simplified. We accomplish
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Thompson-like characterization of solubility for products of finite groups Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-26 P. Hauck, L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos
A remarkable result of Thompson states that a finite group is soluble if and only if all its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory of groups, aiming for global properties of groups from local properties of two-generated (or more generally, n-generated) subgroups. We contribute an extension
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Multiexponential maps in Carnot groups with applications to convexity and differentiability Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-25 Annamaria Montanari, Daniele Morbidelli
We analyze some properties of a class of multiexponential maps appearing naturally in the geometric analysis of Carnot groups. We will see that such maps can be useful in at least two interesting problems: first, in relation to the analysis of some regularity properties of horizontally convex sets. Then, we will show that our multiexponential maps can be used to prove the Pansu differentiability of
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Nonemptiness and smoothness of twisted Brill–Noether loci Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-25 George H. Hitching, Michael Hoff, Peter E. Newstead
Let V be a vector bundle over a smooth curve C. In this paper, we study twisted Brill–Noether loci parametrising stable bundles E of rank n and degree e with the property that \(h^0 (C, V \otimes E) \ge k\). We prove that, under conditions similar to those of Teixidor i Bigas and of Mercat, the Brill–Noether loci are nonempty and in many cases have a component which is generically smooth and of the
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On first-order hyperbolic partial differential equations with two internal variables modeling population dynamics of two physiological structures Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-20 Hao Kang, Xi Huo, Shigui Ruan
In this paper we develop fundamental theories for a scalar first-order hyperbolic partial differential equation with two internal variables which models single-species population dynamics with two physiological structures such as age–age, age–maturation, age–size, and age–stage. Classical techniques of treating structured models with a single internal variable are generalized to study the double physiologically
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On three-dimensional geophysical capillary–gravity water flows with constant vorticity Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-20 Lili Fan, Hongjun Gao
Consideration in this paper is three-dimensional capillary–gravity water flows governed by the geophysical water wave equations with all the Coriolis terms being retained. It is proved that the merely possible flow exhibiting a constant vorticity vector captures vanishing vertical velocity, constant horizontal velocity and flat free surface.
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Optimal exponentials of thickness in Korn’s inequalities for parabolic and elliptic shells Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-19 Peng-Fei Yao
We consider the scaling of the optimal constant in Korn’s first inequality for elliptic and parabolic shells which was first given by Grabovsky and Harutyunyan with hints coming from the test functions constructed by Tovstik and Smirnov on the level of formal asymptotic expansions. Here, we employ the Bochner technique in Remannian geometry to remove the assumption that the middle surface of the shell
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Ultradifferentiable Chevalley theorems and isotropic functions Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-17 Armin Rainer
We prove ultradifferentiable Chevelley restriction theorems for a wide range of ultradifferentiable classes. As a special case we find that isotropic functions, i.e., functions defined on the vector space of real symmetric matrices invariant under the action of the special orthogonal group by conjugation, possess some ultradifferentiable regularity if and only if their restriction to diagonal matrices
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Three-dimensional homogeneous critical metrics for quadratic curvature functionals Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-17 M. Brozos-Vázquez, E. García-Río, S. Caeiro-Oliveira
We show the existence of non-Einstein homogeneous critical metrics for any quadratic curvature functional in dimension three.
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Mollifier smoothing of C 0 -Finsler structures Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-17 Ryuichi Fukuoka, Anderson Macedo Setti
A C0-Finsler structure is a continuous function \(F:TM \rightarrow [0,\infty )\) defined on the tangent bundle of a differentiable manifold M such that its restriction to each tangent space is an asymmetric norm. We use the convolution of F with the standard mollifier in order to construct a mollifier smoothing of F, which is a one-parameter family of Finsler structures \(F_\varepsilon\) that converges
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The obstacle problem for degenerate doubly nonlinear equations of porous medium type Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-17 Leah Schätzler
We prove the existence of nonnegative variational solutions to the obstacle problem associated with the degenerate doubly nonlinear equation $$\begin{aligned} \partial _t b(u) - {{\,\mathrm{div}\,}}(Df(Du)) = 0, \end{aligned}$$ where the nonlinearity \(b :\mathbb {R}_{\ge 0} \rightarrow \mathbb {R}_{\ge 0}\) is increasing, piecewise \(C^1\) and satisfies a polynomial growth condition. The prototype
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The semi-classical limit with a delta potential Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-13 Claudio Cacciapuoti, Davide Fermi, Andrea Posilicano
We consider the semi-classical limit of the quantum evolution of Gaussian coherent states whenever the Hamiltonian H is given, as sum of quadratic forms, by \( H= -\frac{{\hbar ^{2}}}{2m}\,\frac{d^{2}\,}{dx^{2}}\,\dot{+}\,\alpha \delta _{0}\), with \(\alpha \in \mathbb R\) and \(\delta _{0}\) the Dirac delta-distribution at \(x=0\). We show that the quantum evolution can be approximated, uniformly
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L 2 -hard Lefschetz complete symplectic manifolds Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-06 Teng Huang, Qiang Tan
For a complete symplectic manifold \(M^{2n}\), we define the \(L^{2}\)-hard Lefschetz property on \(M^{2n}\). We also prove that the complete symplectic manifold \(M^{2n}\) satisfies \(L^{2}\)-hard Lefschetz property if and only if every class of \(L^{2}\)-harmonic forms contains a \(L^{2}\) symplectic harmonic form. As an application, we get if \(M^{2n}\) is a closed symplectic parabolic manifold
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Timelike minimal Lagrangian surfaces in the indefinite complex hyperbolic two-space Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-05 Josef F. Dorfmeister, Shimpei Kobayashi
It has been known for some time that there exist 5 essentially different real forms of the complex affine Kac–Moody algebra of type \(A_2^{(2)}\) and that one can associate 4 of these real forms with certain classes of “integrable surfaces,” such as minimal Lagrangian surfaces in \(\mathbb {CP}^2\) and \(\mathbb {CH}^2\), as well as definite and indefinite affine spheres in \({\mathbb {R}}^3\). In
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Existence and uniqueness of solutions to some singular equations with natural growth Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-01 Francescantonio Oliva
We study existence and uniqueness of nonnegative solutions to a problem which is modeled by $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\Delta _p u = u^{-\theta }|\nabla u|^p + fu^{-\gamma }& \text {in}\, \Omega , \\ u=0 & \text {on}\ \partial \Omega , \end{array}\right. } \end{aligned}$$ where \(\Omega\) is an open bounded subset of \({\mathbb {R}}^N\) (\(N\ge 2\)), \(\Delta _p\) is
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Quasilinear equations involving indefinite nonlinearities and exponential critical growth in $${\mathbb {R}}^N$$RN Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-01 Luciana R. de Freitas, Jefferson Abrantes Santos, Uberlandio B. Severo
In this work, we establish the existence of nonzero solutions for a class of quasilinear elliptic equations involving indefinite nonlinearities with exponential critical growth of Trudinger–Moser type. Our proofs rely on variational arguments in a Orlicz–Sobolev space with a version of the Trudinger–Moser inequality.
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Balanced metrics and Berezin quantization on Hartogs triangles Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-06-01 Enchao Bi, Guicong Su
In this paper, we study balanced metrics and Berezin quantization on a class of Hartogs domains defined by \(\varOmega _n=\{(z_1,\ldots ,z_n)\in {\mathbb {C}}^n:\vert z_1\vert<\vert z_2\vert<\cdots<\vert z_n\vert <1\}\) which generalize the so-called classical Hartogs triangle. We introduce a Kähler metric \(g(\nu )\) associated with the Kähler potential \(\varPhi _n(z):=-\sum _{k=1}^{n-1}\nu _k\ln
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Order topology on orthocomplemented posets of linear subspaces of a pre-Hilbert space Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-31 D. Buhagiar, E. Chetcuti, H. Weber
Motivated by the Hilbert-space model for quantum mechanics, we define a pre-Hilbert space logic to be a pair \((S,{\mathscr {L}})\), where S is a pre-Hilbert space and \({\mathscr {L}}\) is an orthocomplemented poset of orthogonally closed linear subspaces of S, closed w.r.t. finite-dimensional perturbations (i.e., if \(M\in {\mathscr {L}}\) and F is a finite-dimensional linear subspace of S, then
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Uniform generalizations of Fueter’s theorem Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-31 Baohua Dong, Tao Qian
Fueter’s theorem (1934) asserts that every holomorphic intrinsic function of one complex variable induces an axial quaternionic monogenic function. Sce (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Nat 23:220–225, 1957) generalizes Fueter’s theorem to the Euclidean spaces \({{\mathbb {R}}}^{n+1}\) for n being odd positive integers. By using pointwise differential computation he asserted that every holomorphic
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Geometric conditions for strict submultiplicativity of rank and border rank Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-25 Edoardo Ballico, Alessandra Bernardi, Fulvio Gesmundo, Alessandro Oneto, Emanuele Ventura
The X-rank of a point p in projective space is the minimal number of points of an algebraic variety X whose linear span contains p. This notion is naturally submultiplicative under tensor product. We study geometric conditions that guarantee strict submultiplicativity. We prove that in the case of points of rank two, strict submultiplicativity is entirely characterized in terms of the trisecant lines
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A Kobayashi and Bergman complete domain without bounded representations Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-24 Nikolay Shcherbina, Liyou Zhang
We construct an unbounded strictly pseudoconvex Kobayashi hyperbolic and complete domain in \({\mathbb {C}}^2\), which also possesses complete Bergman metric, but has no nonconstant bounded holomorphic functions.
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Orbits of bounded bijective operators and Gabor frames Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-20 Rosario Corso
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of \(L^2(\mathbb {R})\), which are made of translations and modulations of one or more windows, are often used in applications. More precisely, the paper deals with a question posed in the last years by Christensen and Hasannasab about the existence of overcomplete
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Greedy energy minimization can count in binary: point charges and the van der Corput sequence Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-18 Florian Pausinger
This paper establishes a connection between a problem in Potential Theory and Mathematical Physics, arranging points so as to minimize an energy functional, and a problem in Combinatorics and Number Theory, constructing ’well-distributed’ sequences of points on [0, 1). Let \(f:[0,1] \rightarrow {\mathbb {R}}\) be (1) symmetric \(f(x) = f(1-x)\), (2) twice differentiable on (0, 1), and (3) such that
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Recognizing a finite group from the generating properties of its subsets Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-06 Andrea Lucchini
We assume to have information about the generating properties of the subsets of a finite group G. In particular, we consider the two following situations. We know, for every subset X of G, whether X is a generating set of G. We know the graph whose vertices are the subsets of G and in which there is an edge connecting X and Y if and only if \(X\cup Y\) is a generating set of G. We discuss how this
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Generalizations of linear fractional maps for classical symmetric domains and related fixed point theorems for generalized balls Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-04 Yun Gao, Sui-Chung Ng, Aeryeong Seo
We extended the study of the linear fractional self maps (e.g., by Cowen–MacCluer and Bisi–Bracci on the unit balls) to a much more general class of domains, called generalized type I domains, which includes in particular the classical bounded symmetric domains of type I and the generalized balls. Since the linear fractional maps on the unit balls are simply the restrictions of the linear maps of the
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A note on the nonexistence of positive supersolutions to elliptic equations with gradient terms Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-02 A. Aghajani, C. Cowan
We prove that if the elliptic problem \(-\Delta u+b(x)|\nabla u|=c(x)u\) with \(c\ge 0\) has a positive supersolution in a domain \(\varOmega \) of \( {\mathrm {R}}^{N\ge 3}\), then c, b must satisfy the inequality $$\begin{aligned} \sqrt{ \int _\varOmega c\phi ^2}\le \sqrt{ \int _\varOmega | \nabla \phi |^2}+\sqrt{ \int _\varOmega \frac{b^2}{4}\phi ^2},\quad \phi \in C_c^\infty (\varOmega ). \end{aligned}$$
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Geophysical water flows with constant vorticity and centripetal terms Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-05-02 Calin Iulian Martin
We consider here three-dimensional water flows governed by the geophysical water wave equations exhibiting full Coriolis and centripetal terms. More precisely, assuming a constant vorticity vector, we derive a family of explicit solutions, in Eulerian coordinates, to the above-mentioned equations and their boundary conditions. These solutions are the only ones under the assumption of constant vorticity
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Entire solutions to sublinear elliptic problems on harmonic NA groups and Euclidean spaces Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-04-30 Ewa Damek, Zeineb Ghardallou
We give necessary and sufficient conditions for the existence of entire solutions bounded or large of the equation \({\mathcal {L}}u - p\psi (u) =0\), where \({\mathcal {L}}\) is either the Laplace operator on \({\mathbb {R}} ^d\), \(d\ge 3\) or the Laplace–Beltrami operator on the harmonic NA group and p is a function whose oscillation tends to zero at infinity at a specified rate. The results apply
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Boundary behaviour of $$\lambda $$λ -polyharmonic functions on regular trees Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-04-29 Ecaterina Sava-Huss, Wolfgang Woess
This paper studies the boundary behaviour of \(\lambda \)-polyharmonic functions for the simple random walk operator on a regular tree, where \(\lambda \) is complex and \(|\lambda |> \rho \), the \(\ell ^2\)-spectral radius of the random walk. In particular, subject to normalisation by spherical, resp. polyspherical functions, Dirichlet and Riquier problems at infinity are solved, and a non-tangential
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Construction of solutions of an supercritical elliptic PDE in low dimensions Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-04-28 Mohamed Ben Ayed, Yessine Dammak
In this paper, we study the supercritical problem \((P_\varepsilon )\): \( -\triangle u=K|u|^{4/(n-2)+\varepsilon }u~ \text{ in } \Omega , ~ u=0 \text{ on } \partial \Omega ,\) where \(\Omega \) is a smooth bounded domain in \(\mathbb {R}^n\), \(n=3,4\), \(\varepsilon \) is a positive real parameter and K is a \(C^4\) positive function on \({\overline{\Omega }}\). Following the ideas of Bahri et al
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Levi flat CR structures on 3D Lie algebras Ann. Mat. Pura Appl. (IF 0.959) Pub Date : 2020-04-27 Giovanni Calvaruso, Francesco Esposito, Domenico Perrone
We completely classify Levi flat CR structures (that is, CR structures with vanishing Levi form) on three-dimensional real Lie algebras, in terms of their algebraic and almost contact properties.
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